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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we construct eight in nite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group SO^-(2n, q). Here q is a power of three. Then we obtain four in nite families of recursive formulas for power moments of Kloosterman sums with square arguments and four in nite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O^-(2n, q).
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참고문헌 (19)
참고문헌 신청
C. Peters / 1992 / The Hasse zeta function of a K3 surface related to the number of words of weight 5 in the Melas codes / J. Reine Angew. Math 432 : 151 ~ 176
D. S. Kim / / Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
D. S. Kim / / Ternary codes associated with O-(2n; q) and power moments of Kloosterman sums with square arguments
D. S. Kim / / Ternary codes associated with symplectic groups and power moments of Kloosterman sums with square arguments
D. S. Kim / 1997 / Gauss sums for O-(2n; q) / Acta Arith 80 (4) : 343 ~ 365
D. S. Kim / / Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
D. S. Kim / / Ternary codes associated with O-(2n; q) and power moments of Kloosterman sums with square arguments
D. S. Kim / / Ternary codes associated with symplectic groups and power moments of Kloosterman sums with square arguments
D. S. Kim / 1997 / Gauss sums for O-(2n; q) / Acta Arith 80 (4) : 343 ~ 365
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